Abstract
We present a smooth approximation for the generalized Fischer–Burmeister function where the 2-norm in the FB function is relaxed to a general p -norm ( p > 1 ), and establish some favorable properties for it — for example, the Jacobian consistency. With the smoothing function, we transform the mixed complementarity problem (MCP) into solving a sequence of smooth system of equations, and then trace a smooth path generated by the smoothing algorithm proposed by Chen (2000) [28] to the solution set. In particular, we investigate the influence of p on the numerical performance of the algorithm by solving all MCPLIP test problems, and conclude that the smoothing algorithm with p ∈ ( 1 , 2 ] has better numerical performance than the one with p > 2 .
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